Properties

Label 6897.f
Number of curves 1
Conductor 6897
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("6897.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6897.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6897.f1 6897a1 [0, -1, 1, -282, -1915] [] 5720 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6897.f1 has rank \(1\).

Modular form 6897.2.a.f

sage: E.q_eigenform(10)
 
\( q + 2q^{2} - q^{3} + 2q^{4} - 3q^{5} - 2q^{6} + 5q^{7} + q^{9} - 6q^{10} - 2q^{12} - 2q^{13} + 10q^{14} + 3q^{15} - 4q^{16} + q^{17} + 2q^{18} + q^{19} + O(q^{20}) \)